Problem: Simplify the following expression: $\dfrac{2z}{6z^4}$ You can assume $z \neq 0$.
$ \dfrac{2z}{6z^4} = \dfrac{2}{6} \cdot \dfrac{z}{z^4} $ To simplify $\frac{2}{6}$ , find the greatest common factor (GCD) of $2$ and $6$ $2 = 2$ $6 = 2 \cdot 3$ $ \mbox{GCD}(2, 6) = 2 $ $ \dfrac{2}{6} \cdot \dfrac{z}{z^4} = \dfrac{2 \cdot 1}{2 \cdot 3} \cdot \dfrac{z}{z^4} $ $\phantom{ \dfrac{2}{6} \cdot \dfrac{1}{4}} = \dfrac{1}{3} \cdot \dfrac{z}{z^4} $ $ \dfrac{z}{z^4} = \dfrac{z}{z \cdot z \cdot z \cdot z} = \dfrac{1}{z^3} $ $ \dfrac{1}{3} \cdot \dfrac{1}{z^3} = \dfrac{1}{3z^3} $